How do I emit light from inside a object?
Cycles is a physically based render, and often the best approach is physical recreation.

Components:


Light source
Light cover


Light Source:

This would simply be an emission shader since it is literally a lightblub or LED. I took the button model, and scaled it down slightly on the X and Y axis. I then drastically scaled it on the z axis, and moved it down so the top of the source would to be flush with the of the panel that the button was set into.



Cover:

The cover allows light to pass through it, and is therefore Translucent so a simple translucent node will do the trick. It is also colored, which can be emulated by giving the translucent node a color:



The shape is also important: I added a small bevel to the edges to help see the look.

Final Image





Note

After some experimentation and some research, I discovered that using Sub Surface Scattering (SSS), and placing the light under the button instead of inside, would produce more accurate and better looking results. And it sure did... it also produced exponentially longer render times... even on GPU (using test build)!

Image with SSS:





The major difference is that the light source is under, not inside the button, and is scaled down on the X and Y axis. This method fixed the artifacts that were occurring on the corners, and is more technically accurate. I'd still use the first one, it is way way faster.